Audio signal encoding or decoding

ABSTRACT

Encoding an audio signal is provided wherein the audio signal includes a first audio channel and a second audio channel, the encoding comprising subband filtering each of the first audio channel and the second audio channel in a complex modulated filterbank to provide a first plurality of subband signals for the first audio channel and a second plurality of subband signals for the second audio channel, downsampling each of the subband signals to provide a first plurality of downsampled subband signals and a second plurality of downsampled subband signals, further subband filtering at least one of the downsampled subband signals in a further filterbank in order to provide a plurality of sub-subband signals, deriving spatial parameters from the sub-subband signals and from those downsampled subband signals that are not further subband filtered, and deriving a single channel audio signal comprising derived subband signals derived from the first plurality of downsampled subband signals and the second plurality of downsampled subband signals. Further, decoding is provided wherein an encoded audio signal comprising an encoded single channel audio signal and a set of spatial parameters is decoded by decoding the encoded single channel audio channel to obtain a plurality of downsampled subband signals, further subband filtering at least one of the downsampled subband signals in a further filterbank in order to provide a plurality of sub-subband signals, and deriving two audio channels from the spatial parameters, the sub-subband signals and those downsampled subband signals that are not further subband filtered.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a Divisional of U.S. patent application Ser. No. 12/397,518 filed Mar. 4, 2009, which is a Divisional of U.S. patent application Ser. No. 10/577,106 filed Apr. 25, 2006, now U.S. Pat. No. 7,519,538, which claims priority from PCT Patent Application Serial No. PCT/IB2004/052226, filed Oct. 28, 2004, all of which are incorporated herein in their entirety by this reference thereto.

The invention relates to encoding an audio signal or decoding an encoded audio signal.

Erik Schuijers, Weaner Oomen, Bert den Brinker and Jeroen Breebaart, “Advances in Parametric Coding for High-Quality Audio”, Preprint 5852, 114^(th) AES Convention, Amsterdam, The Netherlands, 22-25 Mar. 2003 disclose a parametric coding scheme using an efficient parametric representation for the stereo image. Two input signals are merged into one mono audio signal. Perceptually relevant spatial cues are explicitly modeled as is shown in FIG. 1. The merged signal is encoded using a mono parametric encoder. The stereo parameters Interchannel Intensity Difference (IHD), the Interchannel Time Difference (ITD) and the Interchannel Cross-Correlation (ICC) are quantized encoded and multiplexed into a bitstream together with the quantized and encoded mono audio signal. At the decoder side, the bitstream is de-multiplexed to an encoded mono signal and the stereo parameters. The encoded mono audio signal is decoded in order to obtain a decoded mono audio signal m′ (see FIG. 2). From the mono time domain signal, a de-correlated signal is calculated using a filter D yielding perceptual de-correlation. Both the mono time domain signal m′ and the de-correlated signal d are transformed to the frequency domain. Then the frequency domain stereo signal is processed with the IID, ITD and ICC parameters by scaling, phase modifications and mixing, respectively, in a parameter processing unit in order to obtain the decoded stereo pair l′ and r′. The resulting frequency domain representations are transformed back into the time domain.

An object of the invention is to provide advantageous audio encoding or decoding using spatial parameters. To this end, the invention provides an encoding method, an audio encoder, an apparatus for transmitting or storing, a decoding method, an audio decoder, a reproduction apparatus and a computer program product as defined in the independent claims. Advantageous embodiments are defined in the dependent claims.

According to a first aspect of the invention, an audio signal is encoded, the audio signal including a first audio channel and a second audio channel, the encoding comprising subband filtering each of the first audio channel and the second audio channel in a complex modulated filterbank to provide a first plurality of subband signals for the first audio channel and a second plurality of subband signals for the second audio channel, downsampling each of the subband signals to provide a first plurality of downsampled subband signals and a second plurality of downsampled subband signals, further subband filtering at least one of the downsampled subband signals in a further filterbank in order to provide a plurality of sub-subband signals, deriving spatial parameters from the sub-subband signals and from those downsampled subband signals that are not further subband filtered, and deriving a single channel audio signal comprising derived subband signals derived from the first plurality of downsampled subband signals and the second plurality of downsampled subband signals. By providing a further subband filtering in a subband, the frequency resolution of said subband is increased. Such an increased frequency resolution has the advantage that it becomes possible to achieve higher audio quality (the bandwidth of a single sub-band signal is typically much higher than that of critical bands in the human auditory system) in an efficient implementation (because only a few bands have to be transformed). The parametric spatial coder tries to model the binaural cues, which are perceived on a non-uniform frequency scale, resembling the Equivalent Rectangular Bands (ERB) scale. The single channel audio signal can be derived directly from the first plurality of downsampled subband signals and the second plurality of downsampled subband signals. However, the single channel audio signal is advantageously derived from sub-subband signals for those downsampled subbands that are further subband filtered, in which case the sub-subband signals of each subband are added together to form new subband signals and wherein the single channel audio signal is derived from these new subband signals and the subbands from the first and second plurality of subbands that are not further filtered.

According to another main aspect of the invention, audio decoding of an encoded audio signal is provided, the encoded audio signal comprising an encoded single channel audio signal and a set of spatial parameters, the audio decoding comprising decoding the encoded single channel audio channel to obtain a plurality of downsampled subband signals, further subband filtering at least one of the downsampled subband signals in a further filterbank in order to provide a plurality of sub-subband signals, and deriving two audio channels from the spatial parameters, the sub-subband signals and the downsampled subband signals for those subbands that are not further subband filtered. By providing a further subband filtering in a subband, the frequency resolution of said subband is increased and consequently higher quality audio decoding can be reached.

One of the main advantages of these aspects of the invention is that parametric spatial coding can be easily combined with Spectral Band Replication (“SBR”) techniques. SBR is known per se from Martin Dietz, Lars Liljeryd, Kristofer Kjorling and Oliver Kunz, “Spectral Band Replication, a novel approach in audio coding”, Preprint 5553, 112^(th) AES Convention, Munich, Germany, 10-13 May 2002, and from Per Ekstrand, “Bandwidth extension of audio signals by spectral band replication”, Proc. 1st IEEE Benelux Workshop on Model based Processing and Coding of Audio (MPCA-2002), pp. 53-58, Leuven, Belgium, Nov. 15, 2002. Further reference is made to the MPEG-4 standard ISO/IEC 14496-3:2001/FDAM1, JTC1/SC29/WG11, Coding of Moving Pictures and Audio, Bandwidth Extension which describes an audio codec using SBR.

SBR is based on the notion that there is typically a large correlation between the low and the high frequencies in an audio signal. As such, the SBR process consists of copying the lower part(s) of the spectrum to the higher part(s) after which the spectral envelope is adjusted for the higher part(s) of the spectrum using little information encoded in the bit stream. A simplified block diagram of such an SBR enhanced decoder is shown in FIG. 3. The bit-stream is de-multiplexed and decoded into core data (e.g. MPEG-2/4 Advanced Audio Coding (AAC)) and SBR data. Using the core data the signal is decoded at half the sampling frequency of the full bandwidth signal. The output of the core decoder is analyzed by means of a 32 bands complex (Pseudo) Quadrature Mirror Filter (QMF) bank. These 32 bands are then extended to full bandwidth, i.e., 64 bands, in which the High Frequency (HF) content is generated by means of copying part(s) of the lower bands. The envelope of the bands for which the HF content is generated is adjusted according to the SBR data. Finally by means of a 64 bands complex QMF synthesis bank the PCM output signal is reconstructed.

The SBR decoder as shown in FIG. 3 is a so-called dual rate decoder. This means that the core decoder runs at half the sampling frequency and therefore only a 32 bands analysis QMF bank is used. Single rate decoders, where the core decoder runs at the full sampling frequency and the analysis QMF bank consists of 64 bands are also possible. In practice, the reconstruction is done by means of a (pseudo) complex QMF bank. Because the complex QMF filter bank is not critically sampled no extra provisions need to be taken in order to account for aliasing. Note that in the SBR decoder as disclosed by Ekstrand, the analysis QMF bank consists of only 32 bands, while the synthesis QMF bank consists of 64 bands, as the core decoder runs at half the sampling frequency compared to the entire audio decoder. In the corresponding encoder however, a 64 bands analysis QMF bank is used to cover the whole frequency range.

Although the invention is especially advantageous for stereo audio coding, the invention is also of advantage to coding signals with more than two audio channels.

These and other aspects of the invention are apparent from and will be elucidated with reference to the embodiments described hereinafter.

In the drawings:

FIG. 1 shows a block diagram of a unit for stereo parameter extraction as used in a Parametric Stereo (“PS”) encoder;

FIG. 2 shows a block diagram of a unit for the reconstruction of a stereo signal as used in a PS decoder;

FIG. 3 shows a block diagram of a Spectral Band Replication (“SBR”) decoder;

FIG. 4 shows a block diagram of combined PS and SBR enhanced encoder according to an embodiment of the invention;

FIG. 5 shows a block diagram of combined PS and SBR enhanced decoder according to an embodiment of the invention;

FIG. 6 shows an M bands downsampled complex QMF analysis (left) and synthesis bank (right);

FIG. 7 shows a magnitude response in dB of a prototype filter;

FIG. 8 shows a magnitude responses in dB of the first four out of 64 non-downsampled complex modulated analysis filters;

FIG. 9 shows a block diagram of a Q bands filter bank with trivial synthesis;

FIG. 10 shows a combined magnitude response in dB of a first non-downsampled modulated QMF filter and 8 bands complex modulated filter bank;

FIG. 11 shows a stylized magnitude response of 4 bands evenly stacked filter bank (top) and oddly stacked filter bank (bottom) according to an embodiment of the invention;

FIG. 12 shows a 77 bands non-uniform hybrid analysis filter bank based on 64 bands complex analysis QMF according to an embodiment of the invention;

FIG. 13 shows a 71 bands non-uniform hybrid analysis filter bank based on 64 bands complex analysis QMF for use in an audio decoder; and

FIG. 14 shows a block diagram of efficient implementation of the complex modulated analysis filter bank

The drawings only show those elements that are necessary to understand the invention.

Combining SBR with PS potentially yields an extremely powerful codec. Both SBR and PS are post-processing algorithms in a decoder consisting of a fairly similar structure, i.e., some form of time to frequency conversion, processing and finally frequency to time conversion. When combining both algorithms, it is required that both algorithms can run concurrently on e.g. a DSP application. Hence, it is advantageous to reuse as much as possible of the calculated intermediate results of one codec for the other. In the case of combining PS with SBR this leads to reusing the complex (Pseudo) QMF sub-band signals for PS processing. In a combined encoder (see FIG. 4) the stereo input signal is analyzed by means of two 64 bands analysis filter banks. Using the complex sub-band domain representation, a PS calculation unit estimates the stereo parameters and creates a mono (sub-band) down-mix is created. This mono down-mix is then fed to an SBR parameter estimation unit. Finally the mono down-mix is converted back to the time domain by means of a 32 bands synthesis filter bank such that it can be coded by the core decoder (core decoder needs only half the bandwidth).

In the combined decoder as shown in FIG. 5, regardless whether or not a dual rate or a single rate system is being used, the full bandwidth (64 bands) subband domain signals after envelope adjustment are converted to a stereo set of subband domain signals according to the stereo parameters. These two sets of sub-band signals are finally converted to the time domain by means of the 64 bands synthesis QMF bank. If one would just combine PS with SBR, the bandwidth of the lower frequency bands of the QMF filter is larger than what is required for a high quality stereo representation. So, in order to be able to give a high quality representation of the stereo image, a further sub-division of the lower sub-band signals is performed according to advantageous embodiments of the invention.

For a better understanding of aspects of the invention, the theory behind complex QMF sub-band filters is first explained.

OMF Sub-Band Filters

The QMF analysis sub-band filter can be described as following. Given a real valued linear phase prototype filter p(ν), an M-band complex modulated analysis filter bank can be defined by the analysis filters

$\begin{matrix} {{{h_{k}(\nu)} = {{p(\nu)}\exp \left\{ {\frac{\pi}{M}\left( {k + {1/2}} \right)\left( {\nu - \theta} \right)} \right\}}},} & (1) \end{matrix}$

for k=0, 1, . . . , M−1. The phase parameter θ is not important for the analysis that follows, but a typical choice is (N+M)/2, where N is the prototype filter order. Given a real valued discrete time signal x(ν), the sub-band signals ν_(k)(n) are obtained by filtering (convolution) x(ν) with h_(k)(ν), and then downsampling the result by a factor M (see left hand side of FIG. 6).

A synthesis operation consists of first upsampling the QMF sub-band signals with a factor M, followed by filtering with complex modulated filters of the type (1), adding up the results and finally taking twice the real part (see right hand side of FIG. 6). Then near-perfect reconstruction of real valued signals can be obtained by suitable design of a real valued linear phase prototype filter p(ν). The magnitude response of the prototype filter as used in the SBR system of the MPEG-4 standard (referred to above) in case of 64 bands is shown in FIG. 7. The magnitude responses of the 64 complex modulated analysis filters are obtained by shifting the magnitude response of the prototype filter p(ν) by

$\frac{\pi}{M}{\left( {k + {1/2}} \right).}$

Part of these responses is shown in FIG. 8. Note that only the positive frequencies are filtered, except for k=0 and k=M−1. As a result the sub-band signals prior to downsampling are close to being analytic, facilitating easy amplitude and phase modifications of real-valued sinusoids. Phase modifications are also possible for the first and last band as long as the sinusoids residing in these bands have a frequency that is above π/2M or below π−π/2M respectively. For frequencies outside this region the performance of phase modification deteriorates rapidly because of interference of the negative frequencies.

Starting from the QMF analysis filters as described above, in embodiments of the invention, a finer frequency resolution is obtained by further filtering each downsampled subband signal ν_(k)(n) into Q_(k) sub-subbands. In the following the properties of the further subband filtering will be derived.

Signal Modification in the Complex QMF Sub-Band Domain

In the following, let Z(ω)=Σ_(n=−∞) ^(∞)z(n)exp(−inω) be the discrete time Fourier transform of a discrete time signal z(n). Assuming the near-perfect reconstruction property as mentioned above and also a design where P(ω), the Fourier transform of p(ν), essentially vanishes outside the frequency interval [−π/M,π/M], which is the case for the prototype filter p(ν) as illustrated above, the next step here is to consider a system where the sub-band signals ν_(k)(n) are modified prior to synthesis. Now, let each sub band k be modified by filtering with a filter B_(k)(ω). With the extending definition

B _(k)(ω)*=B _(−1−k)(−ω). for k<0,  (2)

where the star denotes complex conjugation, it can then be shown (neglecting overall delay, assuming a real valued input and a single rate system) that the resulting system including filter bank synthesis corresponds to a filtering with the filter

$\begin{matrix} {{B(\omega)} = {\sum\limits_{k = {- M}}^{M - 1}{{B_{k}\left( {M\; \omega} \right)}{{{P\left( {\omega - {{\pi \left( {k + {1/2}} \right)}/M}} \right)}}^{2}.}}}} & (3) \end{matrix}$

According to the hypotheses regarding the properties of P(ω), inserting B_(k)(ω)=1 for all kin (3) leads to B(ω)=1, and a squared sum identity follows for the shifted prototype filter responses. By choosing real-valued constants B_(k)(ω)=b_(k)≧0 the system acts as an equalizer, which interpolates the gain values b_(k) at frequencies π(k+1/2)/M. The attractive feature is that the overall system is time-invariant, that is, free of aliasing, in spite of the use of down- and upsampling. This will of course only be true up to the amount of deviation to the stated prototype filter hypotheses.

In order to derive a mono audio signal, additional sub-filtering of the complex sub-band signals should not only preserve these properties, but also extend these properties to manipulation of the filtered sub-band signals. Sub-filtering preserving these properties can be performed using a modification of so-called Mth band filters as known per se from P. P. Vaidyanathan, “Multirate systems and filter banks”, Prentice Hall Signal Processing Series, 1993, sections 4.6.1-4.6.2).

Modulated Filter Banks with Trivial Synthesis

A discrete time signal ν(n) can be split into Q different signals by a bank of filters with impulse responses g_(q)(n), q=0, 1, . . . , Q−1. This is illustrated in FIG. 9. Let the corresponding analysis outputs be y_(q)(n), and consider the trivial synthesis operation

$\begin{matrix} {{y(n)} = {\sum\limits_{q = 0}^{Q - 1}{{y_{q}(n)}.}}} & (4) \end{matrix}$

Perfect reconstruction, y(n)=ν(n), is then obtained by choosing the filters such that

$\begin{matrix} {{{\sum\limits_{q = 0}^{Q - 1}{g_{q}(n)}} = {\delta (n)}},} & (5) \end{matrix}$

where δ(n)=1 if n=0, and δ(n)=0 if n≠0. For causal filters, the right hand side of (5) would have to be replaced with δ(n−d) where d is a positive delay, but this straightforward modification is omitted for clarity of exposition. The filters g_(q)(n) can be chosen as complex modulations of a prototype filter g(n) through

$\begin{matrix} {{g_{q}(n)} = {{g(n)}\exp {\left\{ {\frac{2\pi}{Q}\left( {q + {1/2}} \right)n} \right\}.}}} & (6) \end{matrix}$

In this preferred embodiment of the invention, the filters are oddly stacked (the factor q+1/2). An advantage of this preferred embodiment will be explained later. Perfect reconstruction (5) is obtained if and only if

g(Qn)=δ(n)/Q.  (7)

A variation of this is the real-valued cosine modulation as

$\begin{matrix} {{{g_{q}(n)} = {{g(n)}\cos \left\{ {\frac{\pi}{Q}\left( {q + {1/2}} \right)n} \right\}}},} & (8) \end{matrix}$

with a real-valued prototype filter g(m) satisfying

g(2Qn)=δ(n)/Q.  (9)

(This is easily obtained by consideration of g_(q)(n)+g_(Q-1-q)(n) in (6).)

Sub-Filtering the Complex-Exponential Modulated Filter Bank

Starting from the QMF analysis filters as described above, a finer frequency resolution is obtained by further filtering each downsampled subband signal ν_(k)(n) into Q_(k) sub-subbands by using one of the modulated structures (6) or (8) above. Denote the resulting output signals y_(q) ^(k)(n), and let g_(q) ^(k)(n) describe the filter bank applied within sub band k. If Q_(k)=1, there is no filtering and g₀ ^(k)(n)=δ(n). A typical application example is the case where M=64, Q₀=8, Q_(k)=4 for k=1,2, and Q_(k)=1 for k>2.

The combined effect of the two filter banks from x(ν) to y_(q) ^(k)(n) can be described as filtering with filters F_(q) ^(k)(ω) followed by downsampling by a factor M, where

F _(q) ^(k)(ω)=H _(k)(ω)G _(q) ^(k)(Mω).  (10)

If the prototype filter response P(w) is essentially zero outside the interval [−π/M, π/M], which is the case for the SBR analysis filters (see FIG. 7), then the filter F_(q) ^(k)(ω) has a single nominal center frequency defined in the complex modulated case by

ω_(k,q)=2π(q+Q _(k) s+½)/(MQ _(k)),  (11)

where s is a integer chosen such that Q_(k) (k−½)≦2(q+Q_(k)s)+1≦Q_(k)(k+ 3/2). For example, as illustrated in FIG. 10, if k=0 and Q₀=8, the values of ω_(0,0),ω_(0, 1), . . . , ω_(0,7) are

$\frac{\pi}{8M}{\left( {1,3,5,7,9,11,{- 3},{- 1}} \right).}$

Signal Modification with Non-Uniform Frequency Resolution

The insertion of sub-subband filter banks as described above does not introduce further downsampling, so the alias-free performance of signal modification as shown above in the case of complex QMF only, is preserved. Consider the general combined operation of M-subband analysis, further subband filtering by using Q_(k) sub-subbands within subband k, filtering of each sub-subband signal y_(q) ^(k)(n) by a filter Λ_(k,q)(ω), synthesis within each subband k by summation, and finally synthesis through the M-band synthesis bank. The overall transfer function of such a system is given by (3) with, for k≧0,

$\begin{matrix} {{{B_{k}(\omega)} = {\sum\limits_{q = 0}^{Q_{k} - 1}{{A_{k,q}(\omega)}{G_{q}^{k}(\omega)}}}},} & (12) \end{matrix}$

For ω>π/(2M), this gives

$\begin{matrix} {{{B(\omega)} = {\sum\limits_{k = 0}^{M - 1}{\sum\limits_{q = 0}^{Q_{k} - 1}{{A_{k,q}\left( {M\; \omega} \right)}{G_{q}^{k}\left( {M\; \omega} \right)}{{P\left( {\omega - {{\pi \left( {k + {1/2}} \right)}/M}} \right)}}^{2}}}}},} & (13) \end{matrix}$

so the throughput response of the sub-subband (k,q) is G_(q) ^(k)(Mω)|P(ω−π(k+½)/M)|². For |ω|≦π/(2M), some care has to be taken due to (2). In this frequency range it holds that

B(ω)=B ₀(Mω)|P(ω−π/(2M))|² +B ₀(−Mω)*|P(ω+π/(2M))|²  (14)

and assuming a real sub-subband prototype filter coefficients, it holds that

G_(q) ⁰(−ω)*=G_(Q) ₀ _(-1-q) ⁰(ω),  (15)

so if the modifying filters are chosen such that

Λ_(0,q)(−ω)*=Λ_(Q) ₀ _(-1-q)(ω),  (16)

then B₀(−Mω)*=B₀(Mω) and the squared sum identity mentioned in connection with (3) leads to

$\begin{matrix} {{B(\omega)} = {{B_{0}\left( {M\; \omega} \right)} = {\sum\limits_{q = 0}^{Q_{k} - 1}{{A_{0,q}\left( {M\; \omega} \right)}{G_{q}^{0}\left( {M\; \omega} \right)}}}}} & (17) \end{matrix}$

for |ω|≦π/(2M), corresponding to a throughput response G_(q) ⁰(Mω) for sub-subband (0, q).

Equations (15) until (17) indicate the desire to discriminate between positive and negative frequencies. This is the reason why oddly stacked (complex) filters are being used for sub-filtering the QMF sub-band signals instead of evenly stacked (complex) filters (see FIG. 11). For evenly stacked filters it is not possible to apply phase modifications of sinusoids residing in the centre filter, i.e., the filter with a centre frequency of zero, as there is no discrimination between positive and negative frequencies possible. Assuming a prototype filter with a response G(ω) band limited to [−2π/Q,2π/Q], with Q the number of bands, for the evenly stacked case the lower limit to which phase modifications can approximately be applied is 2π/Q, whereas for the oddly stacked case the lower limit to which phase modifications approximately can be applied is π/Q.

As mentioned in the introduction, for PS synthesis important special cases of the above are equalization and phase modification. For equalization, Λ_(k,q)(ω)=a_(k,q)≧0 and the condition (16) reduces to

a _(0,q) =a _(0,Q) ₀ _(-1-q).  (18)

The phase modification case corresponds to Λ_(k,q)(ω)=exp(iα_(k,q)) in which case the condition (16) is satisfied if

α_(0,Q) ₀ _(-1-q)=α_(0,q).  (19)

Stereo Parameter Estimation

The non-uniform complex filter bank, i.e. the QMF bank followed by the further subband filtering, as described above, can be applied to estimate the stereo parameters Inter-channel Intensity Differences (ID), Inter-channel Phase Differences (IPD) and Inter-channel Cross Correlation (ICC) as shown below. Note that in this practical embodiment, IPD is used as a practically equivalent substitute for the ITT) as used in the paper of Schuijers et al. In the combined PS encoder (see FIG. 4) the first three complex QMF channels are sub-filtered so that in total 77 complex-valued signals are obtained (see FIG. 12).

From this point on the 77 complex-valued time-aligned left and right sub-subband signals are denoted as l_(q) ^(k)(n) and r_(q) ^(k)(n) respectively, accordingly the indexing of y_(q) ^(k)(m).

To estimate the stereo parameters at a certain sub-band sample position n′ the left, right and non-normalized cross-channel excitation are calculated as:

$\begin{matrix} {\mspace{79mu} {{{e_{l}(b)} = {\sum\limits_{q = q_{l}}^{q_{h}}{\sum\limits_{k = k_{l}}^{k_{h}}{\sum\limits_{n = 0}^{L - 1}{{h^{2}(n)}\left( {{{l_{q}^{k}\left( {n^{\prime} - \frac{L}{2} + 1 + n} \right)}}^{2} + ɛ} \right)}}}}}\mspace{20mu} {{e_{r}(b)} = {\sum\limits_{q = q_{l}}^{q_{h}}{\sum\limits_{k = k_{l}}^{k_{h}}{\sum\limits_{n = 0}^{L - 1}{{h^{2}(n)}\left( {{{r_{q}^{k}\left( {n^{\prime} - \frac{L}{2} + 1 + n} \right)}}^{2} + ɛ} \right)}}}}}{{e_{R}(b)} = {\sum\limits_{q = q_{l}}^{q_{h}}{\sum\limits_{k = k_{l}}^{k_{h}}{\sum\limits_{n = 0}^{L - 1}{{h^{2}(n)}\left( {{{l_{q}^{k}\left( {n^{\prime} - \frac{L}{2} + 1 + n} \right)}{r_{q}^{k^{*}}\left( {n^{\prime} - \frac{L}{2} + 1 + n} \right)}} + ɛ} \right)}}}}}}} & (20) \end{matrix}$

for every stereo bin b, h(n) is the sub-band domain window with length L, εa very small value preventing division by zero (e.g. ε=1e−10) and l_(q) ^(k)(n) and r_(q) ^(k)(n) the left and right sub-subband domain signals. In case of 20 stereo bins, the summation over k from k_(l) up to and including k_(h) and q from q_(l) up to and including q_(h) goes as shown in Table. Note that the ‘negative’ frequencies (e.g. k=0 with q=4 . . . 7) are not included in the parameter estimation of (20).

TABLE 1 Start and stop indices of summation over k and q b k_(l) k_(h) q_(l) q_(h) Pass-band frequency region 0 0 0 0 0 0-π/256 1 0 0 1 1 π/256-2π/256 2 0 0 2 2 2π/256-3π/256 3 0 0 3 3 3π/256-π/64 4 1 1 2 2 π/64-3π/128 5 1 1 3 3 3π/128-2π/64 6 2 2 0 0 2π/64-5π/128 7 2 2 1 1 5π/128-3π/64 8 3 3 0 0 3π/64-4π/64 9 4 4 0 0 4π/64-5π/64 10 5 5 0 0 5π/64-6π/64 11 6 6 0 0 6π/64-7π/64 12 7 7 0 0 7π/64-8π/64 13 8 8 0 0 8π/64-9π/64 14 9 10 0 0 9π/64-11π/64 15 11 13 0 0 11π/64-14π/64 16 14 17 0 0 14π/64-18π/64 17 18 22 0 0 18π/64-23π/64 18 23 34 0 0 23π/64-35π/64 19 35 63 0 0 35π/64-π

The summations to calculate e_(l)(b), e_(r)(b) and e_(R)(b) are aligned such that the mid-point of these signals in the summation coincides with the parameter position, hence the shift by

${- \frac{L}{2}} + 1.$

As is clear from Table 1, only sub-subband signals and subband signals with a positive centre frequency are used for estimating stereo parameters. The IID, denoted as I(b), the ICC, denoted as C(b) and the IPD, denoted as P(b) for each stereo bin b are calculated as:

$\begin{matrix} {{{I(b)} = {10{\log_{10}\left( \frac{e_{l}(b)}{e_{r}(b)} \right)}}}{{C(b)} = \frac{{e_{R}(b)}}{\sqrt{{e_{l}(b)}{e_{r}(b)}}}}{{P(b)} = {\angle \; {e_{R}(b)}}}} & (21) \end{matrix}$

The angle in the equation P(b)=∠e_(R)(b) is calculated using the four quadrant arctangent function giving values between −π and π. Depending on target bit rate and application, these parameters, or a subset of these parameters are quantized and coded into the PS part of the bit-stream.

Stereo Signal Synthesis

In order to keep the computational costs (in terms of RAM usage) in the decoder as low as possible a similar analysis structure is used. However the first band is only partially complex (see FIG. 13). This is obtained by summation of the middle band pairs G₂ ⁰(ω) and G₅ ⁰(ω) and G₃ ⁰(ω) and G₄ ⁰(ω). Furthermore, the second and the third band are two-band real-valued filter banks, which is obtained by summation of the output of G_(k) ⁰(ω) and G_(k) ³(ω), and summation of the output of G_(l) ^(k)(ω) and G₂ ^(k)(ω) (see also the discussion in the section about modulated filter banks). Using this simplification of the decoder filter-bank structure, still the discriminative feature between positive and negative frequencies is maintained by subdivision of the first sub-band filter. The decoder analysis filter bank is shown in FIG. 13. Notice that the indexing of the first QMF filtered (sub-)subband signals is sorted according to frequency.

The stereo (sub-)subband signals of a single frame are constructed as:

l _(k)(n)=Λ₁₁ s _(k)(n)+Λ_(N) d _(k)(n)

r _(k)(n)=Λ₁₂ s _(k)(n)+Λ₂₂ d _(k)(n)  (22)

r _(k)(n)=l _(k)(n)e ^(jP) ^(rt)

r _(k)(n)=r _(k)(n)e ^(−jP) ^(rt)   (23)

with s_(k)(n) the mono (sub-)subband signals, and d_(k)(n) the mono de-correlated (sub-) subband signals that are derived from the mono (sub-)subband signals s_(k)(n) in order to account for synthesizing the ICC parameters, k=0, . . . , K−1 the sub-band index (K is the total number of sub-bands, i.e., K=71), QMF sub-band sample index n=0, . . . , N−1 with N the number of sub-band samples of a frame, Λ₁₁, Λ₁₂, Λ₂₁, Λ₂₂ the scale factor manipulation matrices and P_(rt) the phase rotation manipulation matrix. The manipulation matrices are defined as function of time and frequency and can be derived straightforwardly from the manipulation vectors as described in the MPEG-4 standard ISO/IEC 14496-3:2001/FPDAM2, JTC1/SC29/WG11, Coding of Moving Pictures and Audio, Extension 2. s_(k)(n) is defined according to FIG. 12 as resulting in FIG. 13:

s ₀(n)=y ₆ ⁰(n)

s ₁(n)=y ₇ ⁰(n)

s ₂(n)=y ₀ ⁰(n)

s ₃(n)=y ₁ ⁰(n)

s ₄(n)=y ₂ ⁰ +y ₅ ⁰(n)

s ₅(n)=y ₂ ⁰(n)+y ₄ ⁰(n)

s ₆(n)=y ₀ ¹(n)+y ₁ ³(n)

s ₇(n)=y ₁ ¹(n)+y ₁ ²(n)

s ₈(n)=y ₀ ²(n)+y ₂ ³(n)

s ₉(n)=y ₁ ²(n)+y ₂ ²(n)

s _(k)(n)=y ₀ ^(k-7)(n) k=10 . . . 70  (24)

Synthesis of the stereo parameters takes place accordingly the indexing of Table 1.

TABLE 1 Parameter indexing table k i(k) Pass-band frequency region 0  1* −2π/256-−π/256 1  0* −π/256-0 2 0 0-π/256 3 1 π/256-2π/256 4 2 2π/256-3π/256 5 3 3π/256-π/64 6 5 3π/128-2π/64 7 4 2π/128-3π/128 8 6 4π/128-5π/128 9 7 5π/128-6π/128 10  8 3π/64-4π/64 11  9 4π/64-5π/64 12  10  5π/64-6π/64 13  11  6π/64-7π/64 14  12  7π/64-8π/64 15  13  8π/64-9π/64 16-17 14  9π/64-11π/64 18-20 15  11π/64-14π/64 21-24 16  14π/64-18π/64 25-29 17  18π/64-23π/64 30-41 18  23π/64-35π/64 42-70 19  35π/64-π The synthesis equations thus look like:

l _(k)(n)=Λ₁₁(i(k),n)s _(k)(n)+Λ₂₁(i(k),n)d _(k)(n)

r _(k)(n)=Λ₁₂(i(k),n)s _(k)(n)+Λ₂₂(i(k),n)d _(k)(n)  (25)

l _(k)(n)=l _(k)(n)e ^(jP) ^(rt) ^((i(k),n))

r _(k)(n)=r _(k)(n)e ^(−jP) ^((i(k),n))   (26)

Note that the sign of P_(rt) changes in the equations above if a * is encountered in the table. This is accordingly equation (19), i.e., the inverse phase rotation has to be applied for the negative frequencies. Efficient Implementation of Modulated Filter Banks with Trivial Synthesis

Given a modulated filter bank with a prototype filter of length L, a direct form implementation would require QL operations per input sample, but the fact that the modulation in (6) is antiperiodic with period Q can be used to split the filtering into a polyphase windowing of L operations followed by a transform of size Q for each input sample. Please note that a polyphase representation as such is known from P. P. Vaidyanathan, “Multirate systems and filter banks”, Prentice Hall Signal Processing Series, 1993, section 4.3). The following provides an advantageous application of such a polyphase representation according to a preferred embodiment of the invention.

The transform is a DFT followed by a phase twiddle, which is of the order of Q log₂ Q, when Q is a power of two. So a large saving is obtained in typical cases where L is much larger than log₂ Q. In the real modulated case (8), antiperiodicity of period 2Q combined with even/odd symmetries around n=0 and n=Q can again be used for polyphase windowing, and the transform kernel is a DCT of type III. A detailed description for the case of complex modulation is given below.

An effective implementation of the sub-subfiltering, using FFT core processing, may be realized using poly-phase decomposition of the prototype filter followed by modulation. Assume a prototype filter g(n) of order N, where N=mQ and m is a positive integer. This condition is not restrictive, since a prototype filter of arbitrary order can be zero padded to fulfill the constraint. The Z-transform of the prototype filter designed for use in a complex modulated system (6) is

$\begin{matrix} {{G(z)} = {\sum\limits_{n = {{- N}/2}}^{N/2}{{g(n)}z^{- n}}}} & (27) \end{matrix}$

This may be expressed in poly-phase notation as

$\begin{matrix} {{{G(z)} = {\sum\limits_{l = 0}^{Q - 1}{{E_{l}\left( z^{Q} \right)}z^{- l}}}}{where}} & (28) \\ {{E_{l}(z)} = {\sum\limits_{n = {{- N}/{({2Q})}}}^{N/{({2Q})}}{{g\left( {{Qn} + l} \right)}z^{- n}}}} & (29) \end{matrix}$

All filters of the filterbank are frequency-modulated versions of the prototypefilter. The Z-transform of the filter g_(q)(n) is given by

$\begin{matrix} {{{G_{q}(z)} = {G\left( {z\; W^{q + \frac{1}{2}}} \right)}}{where}} & (30) \\ {W = ^{{- j}\frac{2\pi}{Q}}} & (31) \end{matrix}$

The expression for the output from one filter is

$\begin{matrix} \begin{matrix} {{Y_{q}(z)} = {{{G_{q}(z)}{V(z)}} = {{{G\left( {zW}^{q + \frac{1}{2}} \right)}{V(z)}} =}}} \\ {= {{\sum\limits_{l = 0}^{Q - 1}{{E_{l}\left( {- z^{Q}} \right)}{V(z)}z^{- l}W^{- \frac{l}{2}}W^{- {ql}}}} =}} \\ {= {\sum\limits_{l = 0}^{Q - 1}{{E_{l}\left( {- z^{Q}} \right)}{V(z)}z^{- l}^{j\frac{\pi}{Q}l}^{j\frac{2\pi}{Q}{ql}}}}} \end{matrix} & (32) \end{matrix}$

By identifying the components of the last sum, it may be seen that the poly-phase components process delayed versions of the input signal, which subsequently are multiplied by a complex exponential. Finally, all the output signals y_(q)(z), q=0. Q−1, are found by applying an inverse FFT (without scaling factor). FIG. 14 shows the layout for the analysis filter bank. Since the poly-phase filters in (29) are non-causal, a proper amount of delay has to be added to all the poly-phase components.

It should be noted that the above-mentioned embodiments illustrate rather than limit the invention, and that those skilled in the art will be able to design many alternative embodiments without departing from the scope of the appended claims. In the claims, any reference signs placed between parentheses shall not be construed as limiting the claim. The word ‘comprising’ does not exclude the presence of other elements or steps than those listed in a claim. The invention can be implemented by means of hardware comprising several distinct elements, and by means of a suitably programmed computer. In a device claim enumerating several means, several of these means can be embodied by one and the same item of hardware. The mere fact that certain measures are recited in mutually different dependent claims does not indicate that a combination of these measures cannot be used to advantage. 

1. A method of decoding an encoded audio signal, the encoded audio signal comprising an encoded single channel audio signal and a set of spatial parameters, the method of decoding comprising: decoding the encoded single channel audio channel to obtain a plurality of downsampled subband signals, and further subband filtering at least one of the downsampled subband signals in a further filterbank in order to provide a plurality of sub-subband signals, wherein a number of downsampled subband signals subjected to the further subband filtering is smaller than a total number of downsampled subband signals so that downsampled subband signals that are not further subband filtered remain.
 2. A method as claimed in claim 1, wherein the further subband filtering is performed on at least the lowest frequency subband signal of the plurality of downsampled subband signals.
 3. A method as claimed in claim 2, wherein the further subband filtering is further performed on at least the next lowest frequency subband signal of the plurality of downsampled subband signals.
 4. A method as claimed in claim 1, wherein the number of sub-subbands in the lowest frequency subband signals is higher than the number of sub-subbands in the next lowest frequency subband signals.
 5. A method as claimed in claim 1, wherein the further subband filter bank is at least partially a complex modulated filter bank.
 6. A method as claimed in claim 1, wherein the further subband filterbank is at least partially a real valued cosine modulated filter bank.
 7. A method as claimed in claim 1, wherein the further subband filter bank is an oddly stacked filter bank.
 8. A method as claimed in claim 1, wherein, in the lowest frequency subband, phase modifications to the sub-subband signals having a negative center-frequency in time domain are determined by taking the negative of the phase modification applied on a sub-subband signal having a positive center-frequency which is in absolute value closest to said negative center-frequency.
 9. A method as claimed in claim 1, wherein the encoded audio signal comprises spectral band replication parameters and wherein a high frequency component is derived from the plurality of downsampled subband signals and the spectral band replication parameters and wherein the two audio channels are derived from the spatial parameters, the sub-subband signals, the downsampled subband signals that are not further subband filtered and the high frequency component.
 10. An audio decoder for decoding an encoded audio signal, the encoded audio signal comprising an encoded single channel audio signal and a set of spatial parameters, the audio decoder comprising: a decoder for decoding the encoded single channel audio channel to obtain a plurality of downsampled subband signals, and a further filter bank for further subband filtering at least one of the downsampled subband signals in a further filterbank in order to provide a plurality of sub-subband signals, wherein a number of downsampled subband signals subjected to the further subband filtering is smaller than a total number of downsampled subband signals so that downsampled subband signals that are not further subband filtered remain.
 11. An apparatus for reproducing an output audio signal, the apparatus comprising: an input unit for obtaining an encoded audio signal, an audio decoder as claimed in claim 10 for decoding the encoded audio signal to obtain the output audio signal, and a reproduction unit, such as a speaker or headphone output, for reproducing the output audio signal.
 12. A computer program product comprising code for instructing a computer to perform the method as claimed in claim
 1. 13. A method of encoding an audio signal, the audio signal comprising a first audio channel and a second audio channel, the method comprising: subband filtering each of the first audio channel and the second audio channel in a complex modulated filterbank to provide a first plurality of subband signals for the first audio channel and a second plurality of subband signals for the second audio channel, downsampling each of the subband signals to provide a first plurality of downsampled subband signals and a second plurality of downsampled subband signals, further subband filtering at least one of the downsampled subband signals in a further filterbank in order to provide a plurality of sub-subband signals, and deriving spatial parameters from the sub-subband signals and from the downsampled subband signals that are not further subband filtered, wherein for each subband that is further subband filtered, the sub-subband signals are added together after scaling and/or phase rotation to form a new subband signal, and wherein the single channel audio signal is derived from these new subband signals and the downsampled subband signals that are not further filtered.
 14. A method of decoding an encoded audio signal, the encoded audio signal comprising an encoded single channel audio signal and a set of spatial parameters, the method of decoding comprising: decoding the encoded single channel audio channel to obtain a plurality of downsampled subband signals, and further subband filtering at least one of the downsampled subband signals in a further filterbank in order to provide a plurality of sub-subband signals, wherein, in the lowest frequency subband, phase modifications to the sub-subband signals having a negative center-frequency in time domain are determined by taking the negative of the phase modification applied on a sub-subband signal having a positive center-frequency which is in absolute value closest to said negative center-frequency.
 15. A method of decoding an encoded audio signal, the encoded audio signal comprising an encoded single channel audio signal and a set of spatial parameters, the method of decoding comprising: decoding the encoded single channel audio channel to obtain a plurality of downsampled subband signals, and further subband filtering at least one of the downsampled subband signals in a further filterbank in order to provide a plurality of sub-subband signals, wherein a number of downsampled subband signals subjected to the further subband filtering is smaller than a total number of downsampled subband signals so that downsampled subband signals that are not further subband filtered remain, wherein the encoded audio signal comprises spectral band replication parameters and wherein a high frequency component is derived from the plurality of downsampled subband signals and the spectral band replication parameters and wherein the two audio channels are derived from the spatial parameters, the sub-subband signals, the downsampled subband signals that are not further subband filtered and the high frequency component. 